On the freeness of anticyclotomic selmer groups of modular forms
Files
Accepted manuscript
Date
2017-07-01
DOI
Authors
Kim, C.
Pollack, R.
Weston, T.
Version
Accepted manuscript
OA Version
Citation
C Kim, R Pollack, T Weston. 2017. "On the freeness of anticyclotomic selmer groups of modular forms." International Journal of Number Theory, Volume 13, Issue 6, pp. 1443 - 1455.
Abstract
We establish the freeness of certain anticyclotomic Selmer groups of modular forms. The freeness of these Selmer groups plays a key role in the Euler system arguments introduced by Bertolini and Darmon in their work on the anticyclotomic main conjecture for modular forms. In particular, our result fills some implicit gaps which appeared in generalizations of the Bertolini-Darmon result to the case where the associated residual representation is not minimally ramified. The removal of such a minimal ramification hypothesis is essential for applications involving congruences of modular forms.